IsTransitive - Maple Help

GroupTheory

 IsTransitive
 determine whether a permutation group is transitive

 Calling Sequence IsTransitive( G )

Parameters

 G - a permutation group

Description

 • A permutation group $G$ (acting on the set$\left\{1,2,\dots ,n\right\}$ is transitive if, for any $\mathrm{\alpha }$ and $\mathrm{\beta }$, there is a permutation $g$ in $G$ for which ${\mathrm{\alpha }}^{g}=\mathrm{\beta }$. Alternatively, $G$ is transitive if it has precisely one orbit.
 • The IsTransitive( G ) command returns true if the permutation group G is transitive, and returns false otherwise. The group G must be an instance of a permutation group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{PermutationGroup}\left(\left\{\left[\left[1,2\right]\right],\left[\left[1,2,3\right],\left[4,5\right]\right]\right\}\right)$
 ${G}{≔}⟨\left({1}{,}{2}\right){,}\left({1}{,}{2}{,}{3}\right)\left({4}{,}{5}\right)⟩$ (1)
 > $\mathrm{IsTransitive}\left(G\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsTransitive}\left(\mathrm{AlternatingGroup}\left(4\right)\right)$
 ${\mathrm{true}}$ (3)

Compatibility

 • The GroupTheory[IsTransitive] command was introduced in Maple 17.